Higher June 2024 Paper 5 Q23
23 In a survey, 50 people are asked which sports they watch.
The results are shown on the Venn diagram.
(a) One person is chosen at random from those that watch athletics.
Find the probability that this person watches only one other sport. [2]
(b) Two of the 50 people are chosen at random.
Show that the probability that one of them watches only football and the other watches only golf is \(\frac{2}{35}\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{9}{16}\) oe | 2 | B1 for answer \(\frac{k}{16}\) or \(\frac{9}{k}\) and must be a proper fraction | Do not accept ratio or words isw conversion/cancelling |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{10}{50} \times \frac{7}{49} + \frac{7}{50} \times \frac{10}{49}\) oe leading to \(\frac{2}{35}\) with no errors in processing seen | 3 | M2 for \([2]\left(\frac{10}{50} \times \frac{7}{49}\right)\) oe or M1 for \(\frac{10}{50}\) oe and \(\frac{7}{49}\) oe or \(\frac{7}{50}\) oe and \(\frac{10}{49}\) oe seen | Award 3 marks for e.g. \(\frac{10}{50} \times \frac{7}{49} = \frac{1}{35}\) and \(\frac{1}{35} \times 2 = \frac{2}{35}\) 0.2 and 0.142 to 0.143 or 0.35 and 0.204… |